What do you know about these three guys?
s(t) - Position
v(t) - Velocity
a(t) - Acceleration
That is their usual names, anyway.
Derivative move down the list. Antiderivative move up. Which do you need.
Can someone help explain how to do this problem?
Pizza Delivery Problem: Ida Livermore starts off on her route. She records her truck's speed, v(t), in mi/hr, at various times, t, in seconds, since she started.
Approximately how far did Ida's truck travel from t=1 to t=9?
It should be integration.
V(t) is in mi/hr, while t is in seconds. And the book answer is in feet.
The units don't tally.
Convert mi/hr into ft/sec.
(1mi/1hr)(5280ft/1mi)(1hr/3600sec) = (5280)/(3600) = 1.4667 ft/sec
V(t) in mph = 5*t^(1/2)
V(t) in ft/sec = (5*1.4667)t^(1/2)
S = (5*1.4667)INT.(1-->9)[t^(1/2)]dt
S = (7.333)(2/3)[t^(3/2)]|(1-->9)
S = (4.888)[9^(3/2) -1^(3/2)]
S = (4.888)[27 -1]
S = 127.088
S = 127 ft.